The Hornets picked up a surprise win in their Premier League clash with the Gunners on Saturday evening, recovering from a goal down to prevail 2-1.
Chelsea suffered a loss by the same scoreline to bottom-placed Crystal Palace on the same day, meanwhile, and Cleverley believes that Watford can now inflict further misery on the defending champions.
"I really feel we are building something here," he told the club's website. "Why not go and beat Chelsea? We go there with confidence. With this squad of players and staff, you look forward to going into work on a Monday. It's a really good bunch of lads.
"So it's a mixture of doing it for them and personally not scoring for a while, a lot of emotion came out in the celebration [against Arsenal]. It was a really good moment."
Watford are fourth in the league table after eight games, one place and two points better off than Chelsea.